Market Structure and Foreign Trade- Elhanan Helpman, Paul Krugman

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title: Market Structure and Foreign Trade : IncreasingReturns, Imperfect Competition, and the InternationalEconomy

author: Helpman, Elhanan.; Krugman, Paul R.publisher: MIT Press

isbn10 | asin: 026258087Xprint isbn13: 9780262580878

ebook isbn13: 9780585113005language: English

subject International economic relations, Industrialorganization (Economic theory) , Economies ofscale, Competition, Imperfect.

publication date: 1987lcc: HF1412.H45 1987eb

ddc: 382subject: International economic relations, Industrial

organization (Economic theory) , Economies ofscale, Competition, Imperfect.

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Market Structure and Foreign TradeIncreasing Returns, Imperfect Competition, and the International Economy

Elhanan Helpman andPaul R. Krugman

The MIT PressCambridge, Massachusetts

London, England

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Seventh printing, 1999 1985 by The Massachusetts Institute of TechnologyAll rights reserved. No part of this book may be reproduced in any form by anyelectronic or mechanical means (including photocopying, recording, or informationstorage and retrieval) without permission in writing from the publisher.This book was set in Apollo by Asco Trade Typesetting Limited, Hong Kong, andprinted and bound in the United States of America.Library of Congress Cataloging in Publication DataHelpman, Elhanan.Market structure and foreign trade.Bibliography: p.Includes index.1. International economic relations. 2. Industrial organization (Economic theory)3. Economies of scale. 4. Competition, Imperfect. I. Krugman, Paul R. II. Title.HF1412.H45 1985 382 84-21823ISBN 0-262-08150-4 (hb) ISBN 0-262-58087-X (pb)

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CONTENTSPreface xiIntroduction 1IPreliminaries

9

1The Factor Proportions Theory

11

1.1 Integrated Equilibrium 121.2 Factor Price Equalization 131.3 Trade Pattern 161.4 Nontraded Goods 191.5 The Volume of Trade 221.6 Unequal Factor Rewards 241.7 Gains from Trade 28References 29

2Technology and Market Structure

31

2.1 Economics of Scale at the Level of the Firm 322.2 Economies of Scale and Market Structure 342.3 External Economies 362.4 Dynamic Scale Economies 382.5 Specific Inputs and Integrated Firms 392.6 Conclusions 40References 40

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IIHomogeneous Products

43

3External Effects

45

3.1 Production Functions 453.2 Resource Allocation within a Representative Country 473.3 Autarky Equilibrium 503.4 Trading Equilibrium 503.5 Gains from Trade 513.6 Trade Structure 553.7 Factor Price Equalization 593.8 Nonuniqueness 633.9 More on Gains from Trade 64References 66

4Contestable Markets

67

4.1 The Concept of Market Contestability 674.2 Integrated Equilibrium 714.3 Trading Equilibrium 724.4 Robustness of Factor Price Equalization 754.5 Unequal Factor Rewards 774.6 Gains from Trade 79Appendix 4A: Existence of Equilibrium 80Appendix 4B: Losses from Trade 81Reference 83

5Oligopoly

85

5.1 Seller Concentration: Partial Equilibrium 865.2 Seller Concentration: General Equilibrium TradePatterns

88

5.3 Seller Concentration: Welfare 965.4 Free Entry 1005.5 Market Segmentation 104References 111

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IIIDifferentiated Products

113

6Demand for Differentiated Products

115

6.1 The General Formulation 1156.2 Love of Variety Approach 1176.3 Ideal Variety Approach 120References 129

7Trade Structure

131

7.1 Behavior of Firms 1327.2 Integrated Equilibrium 1347.3 Trade Patterns: Free Entry 1407.4 Unequal Factor Rewards 1437.5 Many Goods and Factors 1447.6 Restricted Entry 1467.7 Predictors of the Intersectoral Pattern of Trade 151References 157

8Trade Volume and Composition

159

8.1 Trade Volumes in the Simple Model 1598.2 Trade Volume: Generalizations 1658.3 Trade Composition in the Simple Model 1688.4 Trade Composition: Generalizations and EmpiricalHypothesis

169

Appendix 8A: Geometric properties of Volume and ShareIsocurves

174

References 178

9Welfare

179

9.1 Basic Considerations 1799.2 S-D-S Preferences 1819.3 Lancaster Preferences 1839.4 Equilibrium Scale and Diversity 1879.5 Trade and Income Distribution 190References 195

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10Transport Costs and Nontraded Goods

197

10.1 The Model with Nontraded Goods 19810.2 Nontraded Goods Produced with Increasing Returns 20110.3 Factor Mobility 20410.4 Transport Costs and Market Size Effects 205References 209

11Intermediate Inputs

211

11.1 Integrated Equilibrium 21111.2 Trading Equilibrium: Tradable DifferentiatedProducts

214

11.3 Trading Equilibrium: Nontraded Intermediates 21711.4 A Generalization: Forward and Backward Linkages 220Appendix 11A: A Model of Differentiation in IntermediateGoods

223

References 224IVMultinational Corporations

225

12Single-Product Firms

227

12.1 The Basic Model 22812.2 Equilibrium in an Integrated Economy 23012.3 The Pattern of Trade 23112.4 The Volume of Trade 23812.5 Intraindustry and Intrafirm Trade 241References 244

13 247

Vertical Integration13.1 The Structure of Production 24713.2 An Integrated Economy 24913.3 Trade Patterns 25013.4 Trade Volumes and Trade Shares 255References 259

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14Summary and Conclusions

261

14.1 The Pattern, Volume, and Composition of Trade 26114.2 Trade and Welfare 26314.3 Future Directions 265

Index 267

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PREFACEIn the last few years trade theorists have finally begun to come to grips with the roleof increasing returns and imperfect competition in the world economy. As participantsin this effort, however, we have come to feel that new theoretical work in this areahas left important gaps and that it has not had the effect it should have. We wrotethis book in order to fill in some of the gaps and to present an integrated view of thetheory. We hope that by presenting an integrated treatment of a variety of issuesinvolving increasing returns, imperfect competition, and international trade, we canhelp make this branch part of the core of trade theory rather than merely a promisingnew area.We offer here a monograph rather than a textbook. Although it reviews and restatesknown results, it also contains a good deal of new work. The chapters on contestablemarkets, oligopolies, welfare, and multinational corporations, for example, areentirely new. New insights and results are also available in chapters that cover olderground, such as the treatment of external economies, intermediate inputs, and tradecomposition. The book is suitable, however, as a supplementary graduate text andfor advanced undergraduate courses. Some of the material is somewhat technical,but most of the main points are made with simple models.The book was written at MIT during the academic year 1983-84. While we werewriting it, Helpman was a visiting professor in the Department of Economics at MIT,on leave from Tel-Aviv University. We received helpful comments on drafts of thebook from Richard Brecher, Avinash Dixit, Wilfred Ethier, Torsten Persson, LarsSvensson, and Martin Weitzmann. Gene Grossman and Assaf Razin provided valuablecomments on chapter 4. In addition the work reflects suggestions made byparticipants in seminars at Columbia, Princeton, Harvard, MIT, Dartmouth, Universityof Western Ontario, and Michigan State. We remain of course fully responsible forany errors.We would like to thank all those who provided comments, as well as the

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gallant typists in the Sloan School of Management, the MIT Department ofEconomics, and the National Bureau of Economic Research who worked on portionsof the book. Finally, we would like to thank our wives, who were tolerant andsupportive through many months of nonstop shop talk.

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Market Structure and Foreign Trade

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INTRODUCTIONWhy do countries trade with each other? What are the effects of international trade?It may seem surprising that these questions are still the subject of debate, close toone hundred and seventy years after the publication of Ricardo's Principles. In thelast few years, however, a long-standing undercurrent of discontent with standardtrade theory has finally surfaced in the form of new models offering alternativeapproaches to international trade. These new approaches break with traditionalanalysis by stressing the importance of increasing returns to scale and imperfectcompetition in understanding how the international economy works. The impact ofthese new approaches on research has been substantial. It was not very long agothat discussions of the relationship between trade and industrial organization had tostart by justifying the juxtaposition of such unrelated fields. Today the border countrybetween the theory of international trade and the theory of industrial structure is oneof the most active areas in international economics.A somewhat disturbing feature of these recent developments, however, has been theproliferation of special models, each with its own assumptions, seeminglyinconsistent not only with traditional trade theory but with each other. Thisproliferation is for the most part a healthy thing, an indication that old assumptionsare being challenged and that innovation is taking place. At some point, however, itbecomes necessary that we attempt a synthesis that defines the common elementsin the variety of new models and at the same time reestablishes some continuitywith older traditions.Our purpose in this book is to provide an integrated approach to the analysis of tradein a world characterized by increasing returns and imperfect competition. By an''integrated approach'' we do not mean a survey. What we have tried to do here issomething more ambitious than simply restating a number of existing models in acommon notation. Instead, we develop a new approach to trade theory (which ofcourse builds on the earlier work of many economists), allowing us to treat a numberof existing models as special cases

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and to treat a number of additional issues as well. Most of the analysis in this book isnew, in both analytical technique and substantive results. At the same time webelieve that our approach reveals a similarity in "deep structure" among models thatmay look quite different on the surface, and it helps clarify the continuity betweentraditional trade theory and new approaches. We hope that our integrated approachwill help move the study of increasing returns and imperfect competition from itscurrent status as a promising new subfield of trade theory into a central position atits core.

Why We Need New Theories of TradeThe traditional general equilibrium approach to international trade is a powerful andelegant intellectual construct, capable of yielding many useful insights about atrading world economy. A proposal that this approach share its position as thecentral element of trade theory with alternative approaches is therefore notsomething to be offered lightly. The only good reason for challenging the traditionalapproach is that it does not seem to do an adequate job of explaining the world andalternative approaches seem to offer an opportunity to do better.We can identify four major ways in which conventional trade theory seems to beinadequate in accounting for empirical observation: its apparent failure to explain thevolume of trade, the composition of trade, the volume and role of intrafirm trade anddirect foreign investment, and the welfare effects of trade liberalization. Let usconsider each of these in turn.Conventional trade theory explains trade entirely by differences among countries,especially differences in their relative endowments of factors of production. Thissuggests an inverse relationship between similarity of countries and the volume oftrade between them. In practice, however, nearly half the world's trade consists oftrade between industrial countries that are relatively similar in their relative factorendowments. Further both the share of trade among industrial countries and theshare of this trade in these countries' imcomes rose for much of the postwar period,even as these countries were becoming more similar by most measures.If differences between countries were the sole source of trade, we would expect thecomposition of trade to reflect this fact. In particular, countries should export goodswhose factor content reflects their underlying resources. This is in fact by and largetrue of countries' net exports. But to casual observation, and on more carefulexamination, actual trade patterns seem to include substantial two-way trade ingoods of similar factor intensity. This "intraindustry" trade seems both pointless andhard to explain from the point of view of a conventional trade analysis.


When we turn to intrafirm trade and direct foreign investment, the problem withconventional trade theory is that it is simply an inappropriate framework. In theperfectly competitive, constant-returns world of traditional theory there are no visiblefirms and thus no way to discuss issues hinging on the scope of activities carried outwithin firms. Again, in reality much international trade consists of intrafirmtransactions rather than arm's-length dealings between unrelated parties, andmultinational firms are a prominent part of the international landscape. We wouldlike to have a trade theory that can both explain why this is so and tell us whatdifference it makes.Finally, studies of trade liberalization seem to suggest that conventional trade theorymisses important aspects of the welfare effects of trade. Standard models associatetrade with a reallocation of resources that increases national income in aggregatebut leaves at least some factors with reduced real income. What seems to havehappened in such important episodes of trade liberalization as the formation of theEEC and the U.S.-Canadian auto pact is quite different, however. Little resourcereallocation took place; instead, trade seems to have permitted an increasedproductivity of existing resources, which left everyone better off.These four empirical weaknesses of conventional trade theory are not its onlyproblems. We emphasize them here, however, because they become understandableonce economies of scale and imperfect competition are introduced into our analysis.

Increasing Returns and Imperfect CompetitionIn reality many industries do not seem to be characterized either by constant returnsor perfect competition. By itself, however, this observation would not make acompelling case for introducing these considerations into trade theory, since alleconomic theories leave out many aspects of reality. The reason for emphasizing therole of increasing returns rather than something else, such as the role of consumerpsychology, is that economies of scale seem to allow a straightforward explanationof our empirical puzzles.Consider first the problem of trade between similar countries. If there are country-specific economies of scale, such trade poses no puzzle. Even if differences in factorrewards or technology do not create an incentive for specialization and trade, theadvantages of large-scale production will still lead countries to specialize and tradewith one another. We will show that specialization and trade will persist even whencountries have identical relative factor endowments for a wide variety of models.Increasing returns also provide a simple explanation of intraindustry trade.


It seems apparent that specialization which takes place to realize economies of scalerather than because of differences in factor rewards can easily involve two-way tradein goods with similar factor content.In part III of this book we will develop an approach to trade in which intraindustrytrade is well defined and show that the importance of this trade is greater, the moresimilar countries are in their resources.The relationship between increasing returns, intrafirm trade, and direct foreigninvestment is more indirect, relying on less well formalized insights, but it still seemsclear. Whenever there are inputs such as headquarters services and intermediategoods that are both produced under increasing returns and specific to particularusers, there will be strong incentives to avoid the problems of bilateral monopoly byintegrating upstream and downstream activities in a single firm. If at the same timethere are incentives, such as differences in factor rewards, for locating upstream anddownstream activities in different countries, the result will be multinational firmsengaging in intrafirm trade.Finally, the experience of trade liberalizations that produce all-round gains withoutsignificant resource reallocation is not all paradoxical in a world characterized byincreasing returns, where intraindustry specialization and trade may produce gains inefficiency through an increased scale of production.Increasing returns then, seem to be useful for explaining important features of theinternational economy. Yet they have only recently been integrated into the basictheory of international trade because except under very special circumstancesincreasing returns are inconsistent with perfect competition. Since there is nogenerally accepted theory of imperfect competition, this has seemed to prevent thestudy of trade in the presence of increasing returns from being more than a collectionof special cases.Even if this were true, it would not be a good reason to ignore the role of economiesof scale and imperfect competition in trade. It is better to have a collection ofexamples that seem to capture what is actually going on than to restrict oneself to afully integrated theory that does not. In any case, although recent theoretical workon international trade has been marked by a proliferation of special assumptions, theinsights gained from this work often seem more general than the particular modelsthat suggest them.In this book we will try to develop an approach to the modeling of trade in a world ofincreasing returns and imperfect competition that confirms the impression of a fairlygeneral set of insights behind the special assumptions of particular models. The

result is still not a general theorythis is not possible until economists agree on ageneral theory of imperfect competition. But we



believe that we have developed an approach that does provide an integratingframework for a variety of special models.

Method of the BookThis book is built around the two classic questions of trade theory: First, whatdetermines the pattern of international trade? Second, is international tradebeneficial? These are not the only questions one might ask, or even the mostrelevant for policy. They have been valuable historically as a way of structuringdiscussion, however, and we use them in the same way here. To answer eachquestion, we have a general method that we apply to a variety of particular models.Our method for the analysis of the trade pattern is to begin by constructing areference point, the "integrated economy." This is a description of what the worldeconomy would look like if factors of production were perfectly mobile; thedescription depends on the underlying assumptions about technology, the structureof production, the behavior of firms, and so on.We then "carve up" this integrated economy into separate countries, and ask thefollowing question: Under what conditions will the integrated economy be reproducedthrough trade? In answering this question, we find what we also learn a great dealabout the pattern of international trade because we can determine what transactionsare needed to offset the fact that the world is divided into countries.For example, to reproduce the integrated equilibrium in a world of constant returns,countries must indirectly trade the services of productive factors by trading goodsproduced with different factor intensitieswhich is the essence of the factorproportions theory of trade. If we add to this world some goods produced withcountry-specific economies of scale, to reproduce the integrated economy, we mustconcentrate production of each such good in a single country, giving an additionalsource of specialization and trade. If there are intermediate inputs that are producedwith economies of scale and are not tradable, then to reproduce the integratedeconomy the trading economy must concentrate production of each such input andall the sectors using that input into an "industrial complex" located in a singlecountry. If the integrated economy contains multiactivity firms, but the distribution ofresources in the trading world leads to a geographical separation of these activities,to reproduce the integrated economy, we must have multinational firms. In eachcase asking what is needed to reproduce the integrated economy is a way ofrevealing the essential role of an international economic linkage.The method just described applies to any number of countries, factors, and


goods. The essential points can be made, however, with two-country, two-factorexamples, which we use liberally throughout the book. These examples have adistinctive geometry; we have found the "parallelograms in a box" diagrammatictechnique extremely useful for building our intuition and hope that others will findthe same.Unfortunately trade does not always lead to reproduction of an integrated economy,and we have no general analysis when it does not. What we can do is twofold: wecan establish the conditions under which the integrated economy is reproduced, andwe can explore what happens when it is not by special cases and examples. Some ofthese special analyses suggest points that have the appearance of being both moregeneral than the examples and important in reality. For example, when markets areseparated by transport costs, which of course prevents reproduction of the integratedequilibrium, we have examples suggesting both a tendency of oligopolistic firms toengage in dumping and a tendency for increasing-returns industries to concentrate incountries with large domestic markets.Turning next to the welfare effects of trade, here we also have a general method.We know that in a world of constant returns and perfect competition gains from tradeare ensured. Once increasing returns and imperfect competition are introduced, thereare both extra sources of potential gain and risks that trade may actually be harmful.Our approach is to derive cost-oriented sufficient conditions for gains from trade. Theform of these sufficient conditions typically reveals key welfare effects over andabove those captured by traditional models. For example, in models with oligopolisticfirms a sufficient condition for gains from trade is that an appropriately weightedaverage of output per oligopolistic firm rises as a result of trade; this conditionreveals that increased competition in oligopolistic industries can be a source of gains.In models with differentiated products the sufficient conditions we derive reveal therole of diversity and scale of production at a global level.For the most part, our sufficient conditions are stated in terms of outcomes of trade.In other words, we show that gains from trade are ensured if, for example, the worldoutput from increasing-returns sectors is on average larger than the domestic outputbefore trade. Ideally we would like to go beyond this to derive predictions abouttrade and welfare from "primitives": tastes, technology, and factor endowments. Thisis more difficult; we study it where possible by special cases and examples.

The Book's StructurePart I of the book lays some groundwork for the analysis. It begins with arestatement of conventional factor proportions theorya restatement that


uses the "integrated economy" as a reference point, however. It then describesseveral alternative strategies for modeling market structure when returns to scaleare not constant.Part II of the book develops approaches to trade based on three different ways ofhandling increasing returns. The first is based on the assumption that economies ofscale are external to firms; the second instead assumes average cost pricingenforced in imperfectly competitive industries by the contestability of markets; thethird assumes noncooperative behavior by oligopolistic firms.Part III of the book introduces a particular approach that has proved very valuable asa tool for thinking about many aspects of international trade. This is the"differentiated products" approach. We begin with some necessary technical tools,then develop a basic analysis of the pattern of trade. We then use the basic analysisto analyze a series of topics: the volume and composition of trade, the welfareeffects of trade, the effects of transport costs, and the role of intermediate inputs.Finally, part IV turns to the theory of multinational firms and intrafirm trade. It beginswith a minimal model of a world economy with direct foreign investment, thendevelops a more complex analysis with vertical integration and intrafirm trade.



IPRELIMINARIESThis book begins with some preparation of the ground. First, in chapter 1, we providean exposition of the most influential conventional approach to trade, the factorproportions theory. This exposition serves in part as a background, but it also servesto introduce some key concepts and techniques that we will use repeatedlythroughout the book. In chapter 2 we explore in general terms how it might bepossible to extend our analysis to allow for increasing returns and imperfectcompetition, and we describe the approaches that will be followed in the rest of thebook.



1The Factor Proportions TheoryThe core of modern analysis of trade is the factor proportions theorythe Heckscher-Ohlin model and its extensions. In this book we go beyond this theory to develop anapproach that allows for many more phenomena than can be encompassed byHeckscher-Ohlin-based models. Our approach builds on a factor proportionsfoundation, however. Indeed, one of our major purposes is to show that many of theinsights gained from traditional theory continue to be useful even in a world whereincreasing returns and imperfect competition are important. Thus we begin this bookwith a brief exposition of the basic elements of the factor proportions approach.We present the theory in a way that is perhaps somewhat unfamiliar, although notnew. Much of the traditional expositional apparatus of trade theory is built around 2 2 2 examples; in our analysis it will generally be important that there be moregoods than factors. This means that it will be useful if from the start we develop aframework suitable for a multidimensional analysis.Our approach builds on a long tradition of research in this area, but it is mostintimately related to the recent treatment in Dixit and Norman (1980, chapter 4).The central idea is to use as a reference point a hypothetical construct, which we willcall the integrated equilibrium. This is defined as the resource allocation the worldwould have if goods and factors were both perfectly mobile. We then ask whether itis possible to achieve the same resource allocation if factors of production areinstead divided up among countries and there is no international factor mobility. Wefind in general that there is a set of allocations of factors to countries for which this ispossible. If factor endowments lie within this set, factor prices will be equalizedthrough trade.If factor prices are equalized, and if countries have identical homothetic preferences,we are then able to deduce a relationship between factor endowments and trade,which was first suggested by Vanek (1968): if we look at the factor servicesembodied in a country's trade, we will find that a country is a



net exporter of the services of factors of which it has a relatively large share of theworld's supply.We will develop this approach in what follows. We will also develop two extensions.First is an extension to a world in which not all goods are traded. Second is anextension to the case where countries' factor endowments do not lie in the factorprice equalization set. We will also discuss gains from trade and the dependence ofthe volume of trade on factor endowments.

1.1 Integrated EquilibriumIn this section we describe the equilibrium of an integrated world economy. Althoughat this stage we need not make restrictive assumptions about preferences, we domake them in anticipation of future needs:1. There are N factors of production which are inelastically supplied. TheN-dimensional vector describes the available quantities of these factorsin the world economy. We will also use N to denotes the set of inputs.2. There are I goods produced with quasi-concave, constant returns to scaleproduction functions. We will also use I to denote the set of goods. Every productionfunction has associated with it a unit cost function:

where w is the N-dimensional vector of input prices (factor rewards).3. Preferences are well behaved and homothetic. As a result the share of spendingon every good is a function only of commodity prices, represented by

where p is an I-dimensional vector of commodity prices.4. There is perfect competition.5. All I goods are produced in the integrated equilibrium.Using these assumptions, the equilibrium conditions for the integrated economy canbe represented in a simple way. It is useful, first, to define for this purpose per unitoutput demand functions for factors of production. As is well known (e.g., see Varian1978, chapter 2), these can be derived from the unit cost functions as follows:

where ali(w) is the use of factor l per unit output of good i.


Using to denote the output level of good i in the integrated equilibrium, theequilibrium conditions are

The first condition states that all goods are priced according to marginal cost, asrequired in a competitive equilibrium. The second condition assures clearing of factormarkets, and the third assures clearing of commodity markets.We need for future use a notation for sectoral factor employment vectors in theintegrated equilibrium. We define therefore

as the vector of employment in sector i in the integrated equilibrium. These vectorshave a simple geometric representation when there are only two factors ofproduction. A three-sector (good) version is illustrated in figure 1.1, in which the firstfactor is labor (L) and the second factor is capital (K). The employment vector isrepresented by OQ1, the employment vector is represented by Q1Q2, and theemployment vector is represented by . In this figure sector 1 is the most capitalintensive, sector 2 employs an intermediate capital/labor ratio, and sector 3 is theleast capital intensive (or the most labor intensive).

1.2 Factor Price EqualizationNow suppose that the world economy is divided into countries, with everycountry j receiving an endowment of factors of production. Assumingthat every country has the same homothetic preferences as summarized by thebudget share functions a1(p), we may ask what is the nature of the set FPE(factor price equalization) of endowment distributions in which everycountry can fully employ its resources, using the techniques of production that areused in the integrated equilibrium. This set is of interest because for everyendowment distribution that belongs to it, the equilibrium price-factor-rewardstructure is the same as in the integrated equilibrium.The last point is easily verified by observing that given the integrated



Figure 1.1

equilibrium w, every firm will employ the integrated equilibrium techniques ofproduction and full employment will prevail in every country. Hence the worldeconomy can produce in the trading equilibrium the output levels , in the sensethat there exist output levels in country j, , such that

Since aggregate world income in this trading equilibrium is equal to the income levelin the integrated equilibrium, and since every country spends the integratedequilibrium budget shares on all goods, then there is commodity market clearing inthe trading equilibrium. This proves that for there is factor price equalization inthe trading equilibrium and the trading equilibrium replicates the integratedequilibrium.We are now in a position to characterize the set FPE for a given number of countriesJ. Formally



Figure 1.2

By defintion, for every country can fully employ its resources when using theintegrated equilibrium techniques of production. In particular, given lij, theseresources are fully employed when the output levels are

,in the trading equilibrium.The set FPE is constructed from convex combinations of the integrated equilibriumsectoral employment vectors, and it has a simple geometrical representation (thealgebra and the two-sector geometry appeared in Travis 1964, chapter 2). It isrepresented by the shaded area in figure 1.2 for the case of two countries, twofactors, and three goods. In this figure O is the home country origin and O* is theorigin of the foreign country. The vectors OQ1, Q1Q2, and Q2O* represent theemployment vectors , , and , respectively, relative to the origin of the homecountry, and the vectors O*Q'1, Q'1Q'2, and Q'2O represent the same employmentvectors relative to the origin of



Figure 1.3

the foreign country. This FPE set is not empty because it always contains thediagonal OO*. Since it is a convex symmetrical set around the diagonal, itsboundaries define the limits of dissimilarity in factor composition which is consistentwith factor price equalization. Hence for sufficiently similiar compositions there isfactor price equalization in the trading equilibrium.It is clear from this analysis that the likelihood of factor price equalization dependson the relative ''size'' of the set FPE. In particular, if this set is of lower dimensionthan N, it is very unlikely that we will observe factor price equalization. This impliesthat an analysis of trade patterns that require FPE makes sense only when thenumber of goods is at least as large as the number of factors.

1.3 Trade PatternWe begin by examining the 2 2 2 model. A typical factor price equalization setfor this model is represented by the parallelogram OQO*Q' in figure 1.3, in which OQis the employment level in the first industry, say X, and QO* is the employment levelin the second industry, say Y, in the integrated equilibrium.Suppose that E describes the distribution of factor endowments. Since E is



above the diagonal OO*, the home country is relatively capital rich. Drawing throughE a negatively sloped line whose slope is wL/wKwhere wi is the reward to factor l, l= L, K, in the integrated equilibriumwe obtain point C as the intersection point of thisline with the diagonal. Point C divides the diagonal into two segments that areproportional to the countries' gross domestic product (GDP) levels. Thus isequal to the relative GDP level of the home country.Now we can choose units of measurement so that , and , where

is the income level of the integrated world economy. In this case, by constructingparallelograms between O and E and O and C, we obtain a representation of thehome country's production and consumption levels. Output of X is , output of Y is

, consumption of X is , and consumption of Y is . It is therefore clear that thehome country, which is relatively capital rich, exports the relatively capital-intensivegood X (the quantity of exports is ), and it imports good Y (the quantity ofimports is ), which is the prediction of the Heckscher-Ohlin model. As usual it isassumed in this discussion that there is no two-way trade in identical goods.One can also use figure 1.3 to describe the net factor content of trade. Since thecomposition of consumption is the same in every country (due to the existence offree and costless trade in all goods and of identical homothetic preferences), thenthe composition of the factor content of consumption is the same in every countryand it is identical to the world endowment . Therefore the vector OC describes thefactor content of consumption in the home country. Hence the vector EC, which is thedifference between the endowment and the implicit consumption of factor services, isthe factor content of net trade flows. It is apparent that the home country is a netimporter of labor services and a net exporter of capital services.When the number of traded goods exceeds the number of factors of production thepattern of production and the pattern of trade are not uniquely determined. Thefactor content of net trade flows is uniquely determined, however (this was noted byTravis 1964, p. 143). We demonstrate this point in figure 1.4.Factor employment levels in the integrated equilibrium are represented by OQ1 inthe first industry, Q1Q2 in the second, and Q2O* in the third. The last twoemployment levels are also represented by and OQ'2, respectively. Now, if E isthe endowment allocation, then , and is one equilibriumproduction configuration, and is another equilibrium productionconfiguration (this type of indeterminancy in production is discussed in detail inMelvin 1968). It is clear from the figure that under the former configuration the homecountry exports


Figure 1.4

good 1 and that it imports it under the latter configuration. However, the vector ofthe factor content of net trade flows is given by EC under every configuration (everyconvex combination of these two configurations is also an equilibrium configuration).This observation justifies the approach of Vanek (1968), who devised a scheme forpredicting the factor content of net trade flows for the case of many goods andfactors, given .Let be the N-dimensional vector of the factor content of country j's net imports,and let sj be the relative size of country j as measured by GDP:

Then

because is the factor content of consumption. Given (balanced trade), somecomponents of are positive, and others are negative. Hence, if we chose thenumbering of factors of production so that



(where for simplicity we disregard possible equalities), then (1.6) implies

that is, country j is a net exporter of the services of the first m factors of productionand a net importer of the services of the last N m factors of production. However, wehave renumbered the factors of production in an increasing order of relativeavailability (as compared to the world economy). Hence country j is a net exporter ofservices of those factors with which it is relatively well endowed and a net importerof services of those factors with which it is relatively poorly endowed.This is a general statement of the factor content version of the Heckscher-Ohlintheory in the presence of factor price equalization. Its empirical validity has beenstudied carefully by Leamer (1984), with the results being favorable to the factorproportions theory.Finally, observe that balanced trade is not required for the validity of Vanek's chainargument. If sj is interpreted as the share of country j in spending rather than inincome, then the chain argument still goes through. However, balanced tradewhichobtains when the share of the country in spending is the same as in incomeensuresthat the share of spending is in between and so that some factor service isimported while some other is exported. Large trade surpluses may make a countryexport all factor services, and large trade deficits may make it import all factorservices.

1.4 Nontraded GoodsOur discussion so far has depended on the assumption that all goods are traded. Forsome purposes, however, it is important to allow for the possibility that there arealso goods that cannot be traded. We begin this section by characterizing the factorprice equalization set in the presence of nontraded goods. Then we show that forendowment allocations that belong to this set, the factor content of net trade vectorsstill obeys Vanek's chain rule.Suppose that the set of goods I can be partitioned into IT and IN, , where IT isthe set of traded goods and IN is the set of nontraded goods. Then, if a division ofthe world economy into J countries is to reproduce the integrated equilibrium, notonly must every country be able to employ its resources fully, using the integratedequilibrium techniques of production, but it must do so by supplying its own demandfor nontraded goods. Given identical homothetic preferences, however, self-sufficiency in nontraded goods requires it to devote to the nontraded sectorsresources in proportion to


where the factor of proportionality is the share of the country in world spending.For the purpose of this section we assume balanced trade, so that the share of acountry in world spending is equal to its share in world income. Under thisassumption the factor price equalization set can be characterized as follows:

By comparing (1.8) with (1.4), it is readily seen that the FPE defined in (1.8) issmaller than the FPE defined in (1.4), because in (1.8) there are more restrictionsimposed on the lij's. These restrictions assure that full employment can be obtainedwhen every country produces its own consumption of nontraded goods. The set FPEdefined in (1.8) is not empty, because like the one defined in (1.4) it contains the"diagonal" (all points generated by Vj proportional to V in all countries).It is clear from the construction of the set FPE in (1.8) that when V belongs to it,there is a trading equilibrium with factor price equalization in which the markets fornontraded goods clear separately in every country. Moreover, since the factorcontent of consumption in in every country (where sj is the share of country j inspending), then (1.6) and (1.7) are applicable, which means that the factor contentof net trade flows obeys Vanek's chain rule.At this stage, however, it should be made clear that the relative size of the factorprice equalization set in the presence of nontraded goods depends on therelationship between the number of traded goods and the number of factors ofproduction. Thus, if this set is to have full dimensionality in factor space, the numberof traded goods needs to be at least equal to the number of factors (e.g., Komiya1967).In the remainder of this section we show how to construct geometrically the factorprice equalization set for the case of two factors, two countries, and three goods, oneof which is nontraded.Consider figure 1.5, in which OQ1, Q1Q2, and Q2O* describe the sectoralemployment levels in the integrated equilibrium. If all goods were traded, then thehexagon would have described the factor price equaliza-


Figure 1.5

tion set. Suppose, however, that the most labor-intensive good, good 3, is nottraded. Then clearly an endowment allocation close to Q2 will not bring about factorprice equalization because the foreign country would not be able to employ fully itsfactors of production with the integrated equilibrium techniques of production, giventhat it has to supply its own demand for good 3. This is seen from the fact that afterthe foreign country allocates to the nontraded sector the required inputs in sector 3,the remaining capital/labor ratio is lower than that used in the traded sectors. Hencefully employment is impossible. This means that the factor price equalization set issmaller than .We now construct the factor price equalization set for the case where the labor-intensive good is not traded. First, let us construct allocation points that belong tothis set and at which the relative size of countries is given by point C. Obviously inthis case an equilibrium requires the employment vector in the nontraded sector, ,to be distributed between the home and foreign country in the proportion . Thisis obtained by drawing through C a line parallel to an imaginary line that connects O*with . The result is PP*, with OP being the employment vector in the nontradedsector of the home country and O*P* being the employment vector in the nontradedsector of the foreign country. It remains to construct feasible allocations ofemployment



Figure 1.6

levels to the traded sectors in both countries. This is achieved by constructing theparallelogram .Now, drawing through C the equal income line BB (whose slope is wL/WK), points onthis line that belong to also belong to FPE. This is represented by the heavypart of BB. Repeating this procedure for every point C on the diagonal OO*, weobtained the factor price equalization set described by the shaded area in figure 1.6.This set is a parallelogram. The breakpoint occurs when, by sliding C in figure 1.5toward O, the southeast end of the part of BB in coincides with , and thebreakpoint occurs when the northwest end of BB in coincides with .If E is the endowment point in figure 1.6, then the vector of factor content of nettrade flows is given by EC, where the slope of the line EC is the relative wage.

1.5 the Volume of TradeOur discussion of the indeterminancy in the pattern of production and trade when thenumber of traded goods exceeds the number of factors of production makes it clearthat in this case the volume of trade is also indeterminate. Therefore in this sectionwe confine attention to the "even" case. In particular,



since the current analysis is designed to serve as background and reference model tothe discussion of trade volumes in the presence of differentiated products (chapter8), we restrict our discussion to the 2 2 2 case.Consider the factor endowments in the factor price equalization set. We want tocompare the dependence of the volume of trade on the factor distribution points. Inparticular, we want to construct equal-volume-of-trade curves.A standard definition of the volume of world trade is the sum of exports acrosscountries. As long as we consider factor endowments in the set FPE, there is nodifference between comparisons of nominal and real trade volumes. Thus in the two-country, two-sector case the volume of trade is

where good X is exported by the home country and good Y is exported by the foreigncountry (X is also the output level of X in the home country and Y* is the output levelof Y in the foreign country). Assuming balanced trade, the volume of trade can berepresented in the following two alternative forms:

Now in the factor price equalization set s is a linear function of home country factorendowments [see (1.5)-] and X is a linear function of home country factorendowments (X is solved from and , where ali are the factorimputs per unit output in the integrated equilibrium). Hence (1.9a) implies

for some (lL, lK), whenever (L, K) is in the factor price equalization set. This meansthat the equal volume of trade curves in the FPE set are straight parallel lines. Inparticular, since the volume of trade is constant and equal to zero on the diagonalOO*, then all equal trade volume lines are parallel to the diagonal( ). These lines are drawn in figure 1.7. It is also easy to check that if(1.10) applies to endowment points above the diagonal, then gL < 0 and gK > 0, andif it applies to points below the diagonal, then gL < 0 and gK > 0 [(1.10) applies topoints above the diagonal if X is relatively capital intensive and to points below thediagonal if X is relatively labor intensive].It is clear from figure 1.7 that the volume of trade is larger, the larger the differenceacross countries in factor composition. This result is intuitively



Figure 1.7

appealing for a model in which differences in factor composition are the sole basis fortrade.We should also note that figure 1.7 implies that in some sense relative country sizehas no effect on the volume of trade.

1.6 Unequal Factor RewardsWe now study the factor content of net trade flows in the absence of factor priceequalization. For this purpose we do not require preferences to be homothetic andidentical across countries; we derive predictions on bilateral trade flows instead ofthe trade flows between a country and the rest of the world.The basic insight (due to Brecher and Choudhri 1982) that serves as a basis for themore general analysis that follows is obtained from figure 1.8 for a two-factor, four-good, and three-country case. It depicts a Lerner diagram in which the isoquants ofthe four goods each represents a Krona worth of output (i.e., the isoquant of good irepresents the output level 1/Pi). For every country j the ray Kj/Lj represents thecapital/labor ratio of its endowment, and the downward sloping line with slope represents its unit cost line.The fact that the more capital per worker a country has, the higher is its



Figure 1.8

wage rental ratio, is established from properties of the maximum gross domesticproduct function (e.g., Dixit and Norman 1980, chapter 2) which is defined as

where fi() is the production function in sector i. II(p, V) is positively linearhomogeneous and concave in V, and the competitive reward to factor l is given by

Hence in the two-factor case an equal gross domestic product curve has the shapeexhibited in figure 1.9, and the slope of this curve equals the competitive wagerental ratio. Apart from possible linear segments, the wage rental ratio rises with thecapital/labor ratio. A proportional exlpansion in the endowment of labor and capitalproduces a radial expansion of the GDP curve,



Figure 1.9

so that the wage rental ratio depends on the composition of factor endowments butnot on their absolute size.In the equilibrium described by figure 1.8, the first country, which has more capitalper worker than the other two, produces goods 1 and 2; the second country, with theintermediate capital/labor ratio, produces goods 2 and 3 (it may share good 2 withcountry 1 and good 3 with country 3); and the third country, which has the smallestamount of capital per worker, produces goods 4 and 3. It is, however, clear from thisfigure that the more capital rich a country is, the more capital and less labor it usesper Krona worth of output in all lines of production. It is also easy to see that theexistence of factor-intensity reversals would not change this result. Henceindependently of the bilateral pattern of trade between a pair of countries, the morecapital-rich country's exports embody more capital per worker than its imports, if wecalculate factor content with the exporter's techniques of production.In order to generalize this result, let Tjk be the vector of commodity imports bycountry j from country k. Then we define the factor content of this import vector by

where



is the vector of factor inputs per unit output. In this definition the techniques ofproduction of the exporter are used to calculate factor content.Competiton implies

with equality holding when good i is produced by country k. Combining (1.12) with(1.11) yields

Now, since

then using this result and (1.11) and (1.12), we obtain

or

The combination of (1.13) and (1.14) implies the following restrictions on the factorcontent of bilateral trade flows (due to Helpman 1984):

Hence country j imports from country k goods whose factor content is large onaverage in factor services that are cheaper in k, and by the same token it exports tok goods whose factor content is large, on average, in factor services that are cheaperin j. In the two-factor case this reduces to the Brecher-Choudhri result.It should be observed that in the presence of many factors the cross-countrydifferences in relative factor rewards is not uniquely determined by differences in thecomposition of factor endowments, as it is in the two-factor case. The link betweenfactor rewards and factor composition is given in this case by

(see Helpman 1984 for a proof). Indeed, this implies in the two-factor case that thecountry with a larger capital/labor ratio cannot have a lower wage/rental ratio.



Equation (1.15) provides a restriction on the factor content of bilateral trade flows forall preference structures. It holds trivially in the presence of factor price equalization,and it is therefore useful only when factor prices are not equalized. Since it dependson trading equilibrium data, it represents a testable hypothesis.

1.7 Gains from TradeOur interest in this section, as well as in most other parts of this book, is inaggregative welfare effects rather in distributional issues. For this reason we considergains from trade for economies with a representative individual. For such economiesgains from trade are ensured if in the trading equilibrium the economy can afford topurchase its autarky consumption vector. Since in autarky consumption equalsproduction, this condition reads

where XA is the economy's autarky output vector, X is its free trade output vector,and p is the free trade price vector.The proof that (1.17) is sufficient for gains from trade is as follows. Let e (p, u) bethe mimimum expenditure function (see Varian 1978, chapter 3).Then, if XA provides the utility level uA, we have

which implies, by (1.17),

If, however, u is the utility level in balanced free trade, then

and we obtain

which implies , thus proving gains from trade.We will use condition (1.17) on several occasions later in the book. At this stage itremains to be shown that it is satisfied in a balanced free trade equilibrium. We willprove this point by means of a method that will be used repeatedly throughout thebook.From (1.12)


However,

and in particular, for , the autarky factor reward vector. Hence

where the last equality is obtained from factor market-clearing conditions [see(1.2)]. But in an economy where there are no pure profits. Hence

which is (1.17).Our proof is rather roundabout, and it serves mainly to introduce the reader to themethod. Condition (1.17) is always satisfied in competitive economies with convextechnologies because the competitive process leads to an allocation of resourceswhose value of output is maximal.

ReferencesBrecher, Richard E., and Choudhri, Ehsan V. ''The Factor Content of InternationalTrade without Factor Price Equalization.'' Journal of International Economics 12(1982):277-283.Dixit, Avinash, and Norman, Victor. Theory of International Trade. Cambridge,England: Cambridge University Press, 1980.Helpman, Elhanan. "The Factor Content of Foreign Trade." Economic Journal 94(1984): 84-94.Komiya, Ryutaro. "Non-Traded Goods and the Pure Theory of International Trade."International Economic Review 8 (1967): 132-152.Learner, Edward E. Sources of International Comparative Advantage: Theories andEvidence. Cambridge, Mass.: The MIT Press, 1984.Melvin, James R. "Production and Trade with Two Factors and Three Goods."American Economic Review 58 (1968):1249-1268.Travis, William P. The Theory of Trade and Protection. Cambridge, Mass.: HarvardUniversity Press, 1964.Vanek, Jaroslav. "The Factor Proportions Theory: The N-Factor Case." Kyklos 24(1968):749-756.Varian, Hal R. Microeconomic Analysis. New York: Norton, 1978.


2Technology and Market StructureLike most traditional trade theory, the factor proportions theory, of internationaltrade described in chapter 1 rests on the simplifying assumption of constant returnsto scale. It has been known for a long time, however, that relaxing the assumption ofa constant-returns technology can have a significant impact on our view of trade.Even while helping create the factor proportions theory, Ohlin (1933) pointed outthat economies of scale in production provide an incentive for internationalspecialization and trade that can supplement the incentives created by cross-countrydifferences in factor endowments and give rise to trade even in the absence of suchdifferences. Yet until recently the assumption of constant returns remained the basisof the bulk of trade theorizing.The reason for the long dominance of trade theories based on a constant-returnstechnology is that as soon as this assumption is relaxed, we must confront the issueof market structure. Except under special circumstances a world where returns toscale are not constant will not be a world of perfectly competitive markets. Sincethere is no generally accepted theory of imperfect competition, it has seemedimpossible to say anything general about trade in a world whose technology allowsfor increasing returns.In subsequent chapters of this book we will analyze international trade under severalalternative assumptions about the nature of competition. We will show that someimportant conclusions about both the positive and normative aspects of trade arevalid for a variety of market structures. This means that it is possible to have atheory of trade in the presence of increasing returns without committing ourselves toany one theory of imperfect competition. Clearly, however, market structure is notcompletely arbitrary. Even if technology does not fully determine the nature ofcompetition, it sets limits on what is possible.The purpose of this chapter is to provide an analysis of the relationship between thecharacteristics of technology and the nature of market structure.



This discussion will be useful as an introduction to some concepts we use later in thebook and as a justification for our choices of issues and assumptions in subsequentchapters.This chapter is in five sections. The first section presents some basic definitions andconcepts. The second describes the major approaches we will take to modelingimperfectly competitive marketscontestable markets, Cournot and Bertrandoligopoly, and monopolistic competition. The third section describes an alternativeapproach that avoids the problem of modeling market structure, the assumption thateconomies of scale are external to firms.In the fourth section we discuss the relationship between the static analysis that weuse in this book and dynamic conceptions of scale economies. Finally, the last sectiondiscusses the role of specific inputs in creating an incentive to form multiproductfirms, which is crucial in explaining the existence of multinational enterprises.

2.1 Economies of Scale at the Level of the FirmThe easiest form of scale economies to give a real-world justification is increasingreturns at the level of an individual firm. Other things equal, a larger firm will bebetter able to overcome indivisibilities, allowing either fuller use of capacity or theuse of more specialized and hence more efficient equipment. At the same time someoverhead costs are independent of the scale of production and thus fall per unit asproduction increases. And simple physics can provide advantages to large scale, forexample, in process industries where the relationship between volume and surfacearea provides an incentive to make pipes, storage tanks, and other implements, aslarge as possible.How important are these internal economies of scale? In the 1950s and early 1960smuch of the quantitative evidence seemed to suggest that in the United States, atleast, such economies were largely exhausted, that optimal plant sizes weregenerally small relative to the market. More recently workers in industrial economicshave revised their assessment of the importance of such scale economies upward(see Scherer 1980). This reflects several factors. First, "industries" often producemany products, so that even when optimal plant size is only a few percent of totalindustry output, there may be many products produced at less than optimal scale.Second, there appear to be important economies of multiplant operation notcaptured by plant-based estimates of scale economies. Third, there are probablyimportant dynamic scale economies internal to firms.We should note, however, that though economists have become more willing toaccept the importance of scale at the level of the firm, other


observeswho have traditionally laid more stress on scale economies thaneconomistshave become more skeptical. Very recent managerial literature nowstresses the problems of incentive, control, and morale which arise as organizationsgrow large and which can outweigh purely technical factors. Nevertheless, there is nodoubt that economies of scale internal to firms are important enough to make theirimplications worth studying. This is particularly true in international economics, sincemost countries have domestic markets much smaller than those of the United States.So far we have used the term economies of scale loosely. It is helpful to have a moreformal statement. Consider a single-product firm which produces output x using avector of inputs v according to the production function

We will say that f() exhibits local economies of scale for l greater than, butsufficiently close to, one. An index of local scale economies is the elasticity of x withrespect to l, evaluated at l = 1:

where fl() is .It will usually be more convenient, however, to work with a cost-based index of scaleeconomies. The production function f() implies a minimum cost function C(w, x),where w is the vector of input prices. An alternative index of economies of scale isthe inverse of the elasticity of cost with respect to output (or, equivalently, the ratioof average to marginal cost):

Not surprisingly, in the vicinity of an optimum position these two measures of scaleeconomies will be equivalent (see Hanoch 1975); that is, at the cost-minimizinginput choices corresponding to a given output and set of factor prices, .It is worth repeating that q() is only a local index of scale economies, which ingeneral depends on both w and x. It will sometimes be useful, however, to assumethat f() is homothetic. When this is true, we can rewrite the function in the form

where is linearly homogeneous in its arguments. When we can do this, we canthink of as an index of "factor input," and as a productivity


effect. Correspondingly we can write the average cost function in the form

where is again linearly homogeneous and can be interpreted as an index of thecost of "factor input."The assumption of homotheticity will often be a helpful simplification, because it willallow us to analyze input choices in terms of the functions or without having toworry about interactions between input choices and the scale of production.The crucial fact about internal economies of scale is of course that if they persist,they are inherently inconsistent with competitive equilibrium. As long as ,marginal cost pricing implies losses. So internal scale economies must be associatedwith a market structure that allows prices above marginal cost. Our next step thenmust be to discuss alternative theories of market structure.

2.2 Economies of Scale and Market StructureThe presence of economies of scale at the level of the firm implies that price-takingbehavior is inconsistent with non-negative profits and thus that markets cannot beperfectly competitive. To go beyond this insight, however, it is necessary to bespecific about how price-setting firms behave. There is no general theory of thebehavior of imperfectly competitive firms, but we will lay out some basic issues anddescribe the particular approaches we will use later in the book.The first question we need to ask is whether firms with market power act in acooperative or a noncooperative fashion. In reality the answer is that there is at leastsome cooperation. Formal cartels and price-fixing arrangements, though illegal in theUnited States, are not uncommon elsewhere and not unknown even where they arenot legal. More generally, tacit cooperation to avoid price wars through priceleadership and other coordinating devices is common. The theory of cooperativebehavior in oligopolistic industries is not well developed, however. Thus in this bookwe will restrict ourselves to an analysis of markets where the participants behavenoncooperatively.Even if we rule out collusion, the outcome of noncooperative behavior by firmsdepends to a considerable extent on additional details. In particular, the outcome ofcompetition in an industry depends on two factors: the strategic variables in terms ofwhich the noncooperative game is played and the conditions of entry into and exitfrom the industry.Most theoretical work on oligopoly assumes that the strategic variables of


firms are either outputsthe Cournot assumptionor pricesthe Bertrand assumption. Inthe first case each firm chooses its profit-maximizing output level, taking other firms'outputs as given. In the second case each firm chooses its profit-maximizing price,taking other firms' prices as given. There has always been a tension between thesetwo approaches. As a description of firm behavior, the Bertrand assumption seems tomost observers to be more realistic. Yet the results that come from Cournot modelsoften seem more plausible. We will make use of both assumptions at different pointsin the book.The issue of entry and exit has also been a major theme in industrial organization.There are two important questions arising from the possibility that new firms couldenter an imperfectly competitive industry. The first is whether entry will eliminateeconomic profits. We will consider both models in which entry eliminates profits andmodels in which barriers to entry allow some pure profits to persists. We will not,however, tackle the second question, which is that of entry deterrence: the measuresthat firms in an industry might take to discourage potential competitors.Bearing in mind these general considerations, in this book we will actually developtheoreis of trade in the presence of three kinds of imperfectly competitive marketstructures:1. Contestable markets. This concept has been promoted by Baumol, Panzar, andWillig (1982) as a benchmark case for the analysis of industry structure. In terms ofour preceding discussion, the theory of contestable markets combines theassumptions of Bertrand behavior by firms and costless unrestricted entry and exit.Although the originators of the concept of contestable markets were largelyinterested in the analysis of multiproduct firms, we will only use it in the case ofsingle-product firms, where it has a simple implication: every good subject toeconomies of scale at the level of the firm will be produced by a single firm, and thatfirm will price the good at average cost. We use the contestable markets theory asthe basis for the analysis in chapter 4.2. Cournot oligopoly. Chapter 5 of the book offers an alternative approach, one basedon the traditional Cournot assumption of noncooperative behavior with outputs asthe strategic variables. We consider both the case where firms earn some pureprofits, and the case where free entry drives profits to zero.3. Monopolistic competition. The monopolistic competition approach is, like thecontestable markets approach, based on the assumption of Bertrand competition:each firm takes competitors' prices as given. We now suppose, however, that firmsare able to differentiate their products so that they are not perfect substitutes foreither the products of existing competitors or the products of potential entrants. Each

firm thus acts as a monopolist facing a downward-sloping demand curve.



Within this approach we consider two alternative cases of entry. The first is onewhere entry is restricted, so that there may be economic profits in imperfectlycompetitive sectors. This case is typically referred to as Bertrand oligopoly. Thesecond case is where there is free entry that drives profits to zero. This last variant isChamberlin's famous "large group" case and is the one we use most.The monopolistic competition approach to market structure can be used to shed lighton a surprisingly wide variety of issues in international economics. Thus we devotethe whole of part II of the book to developing this approach and applying it. Furtherthe analysis of multinational firms in part III also assumes a monopolisticallycompetitive market structure.

2.3 External EconomiesAlthough most of this book will be concerned with the analysis of trade under themarket structures just described, we will actually begin our analysis of trade underincreasing returns with the one case where increasing returns are consistent withperfect competition. This is the case where returns to scale are constant at the levelof the firm, and social increasing returns take the form of external economies. Wedevote only one chapter to this case. Until recently, however, external effects werethe standard way to introduce scale economies into international trade. Thus theuses and limitations of the approach need some discussion.In principle, external effects can arise from any economic activity. Thus a generalexternal economy model would have production functions at the firm level of theform:

where x is a vector of all possible "external" influences. The traditional formulationhas assumed that the only relevant element of x is the output of the domesticindustryfor example, Japanese productivity in computers depends on the size of theJapanese computer industry. More generally, however, the vector of external effectssurely need not be restricted either to industry-specific or country-specific variables.Japanese computer productivity could easily depend both on the size of the U.S.computer industryan international external effectand on the size of Japan'ssemiconductor industryan interindustry effect.Still, the usual assumption is that the relevant external effect is of the output of thenational industry on the productivity of individual firms within that industry. Thisallows us to have constant returns from the point of view of any


individual , where X is the industry's outputwhile having increasingreturns form the point of view of the industry as a whole. The usual formulation is infact to assume that scale effects enter multiplicatively:

where exhibits constant returns. In either the special form (2.5) or a more generalform, the external economies assumption lets us write an industry productionfunction X = F(v), which exhibits increasing returns, with an assumption of averagecost pricing.But how does one justify the way industry output enters into the firm's productionfunction? One justification, invoked by authors from Marshall (1920) to Ethier (1979),is the argument that a larger industry is able to support production of a wider varietyof intermediate inputs at lower cost. If this is the reason for industry economies ofscale, however, the problem of handling the effects of scale economies on marketstructure has not really been solved. Rather, it has been concealed through anincomplete specification of the model. As we will show in chapter 11, certain specialassumptions about the market structure of the intermediate goods industry cancause the economy to behave "as if" there are true technological externaleconomies, but this is by no means a general result.A second potential justification for the external economy type of model is to arguethat it is really an internal economy story in which something is constraining firms toprice at average cost. As we have already mentioned, the threat of entry bycompetitors can, under some hypotheses about behavior, lead to average costpricing by monopolists. As we will show in chapter 4, however, average cost pricingimposed by the threat of entry is not always the same in its implications forinternational trade as average cost pricing resulting from perfect competition andconstant private returns to scale.Finally, it is possible to argue that there are external economies resulting from theinability of firms to appropriate knowledge completely. Information gained by onefirm, whether through explicit R & D (research and development) or throughexperience, will often be acquired by the firms through word of mouth or deliberate"reverse engineering." This is a true externality; however, it is hard to envisage itleading to a relationship such as (2.4). In the first place innovative industries willordinarily not be perfectly competitive. Further an emphasis on the generation ofknowledge points one in the direction of a dynamic rather than a purely static model.Given these objections, it seems that one should regard the static externaleconomies model as at best a rough proxy for more complex models. This does


not mean that models that assume pure external economies cannot yield usefulinsights. It does mean that they should be used cautiously and that the resultsshould always be checked for plausibility, given the underlying explanations ofincreasing returns.One question for which this appeal to the implicit underlying model is especiallyimportant is the question of the unit to which external economies apply. Traditionallythis has been assumed to be the nation. Still, as Ethier (1979) has pointed out, if"external" economies arise from economies of scale in the production of intermediategoods, and if these intermediates are (cheaply) tradable, we should think ofeconomies of scale as applying at the international rather than the national level.The key point here is that it is the tradability of the intermediate goods that iscrucial. Where intermediate inputs are not tradable, the scale economies arenational, not international. This point comes out clearly in the explicit model of tradewith intermediate goods developed in chapter 11, but the point can easily be missedif the underlying model of production and market structure is concealed within anexternal economies formulation.A similar source of potential confusion arises if external economies are assumed toresult from incomplete appropriability of knowledge. In this case the question ofwhich unit is relevant for externalities depends crucially on the details of howinnovations diffuse. If information spreads by word of month, the relevant unit will bea nation or an even smaller unitsay, the Boston metropolitan area. If, on the otherhand, firms can reap the benefits of other firms' innovations by taking their productsapart and seeing how they work, external economies should be thought of asinternational in their effect.Despite these criticisms the external economies approach to incorporating increasingreturns remains useful. It should, however, be demoted from its traditional positionas the basic approach to trade with economies of scale.

2.4 Dynamic Scale EconomiesIn practice, it is likely that one of the most important sources of economies of scale(and of imperfect competition) lies in the dynamic process by which firms andindustries improve their technologies. Recent industrial organization literature hasemphasized the role of the learning curve in generating industry concentration,whereas the most plausible accounts of external economies involve diffusion ofknowledge, and inherently dynamic issue.We do not attempt in this book to do any explicit modeling of dynamic scaleeconomies. To a degree we believe that our static models can proxy for these

dynamic effects. However, the interpretation of this proxy role must be made



carefully. There are major potential pitfalls in mixing static and dynamic analysis.The most important danger is in misinterpreting the nature of the mapping fromdynamics into statics. To the extent that a static model is used as a proxy for adynamic world, it should be viewed as a representation of the whole time path ofthat world, not a snapshot at a particular point in time.It particular, the comparison of equilibria involved in comparative staticsexercisessuch as the comparison of autarky with free tradeshould be understood as acomparison between two alternative histories, not as a change that takes place overtime. We will often follow the common shortcut of talking about "before trade"versus "after trade," but what we really mean is "if trade had not been allowed"versus "if trade had been allowed."This is not a pedantic point, because even careful theorists sometimes get it wrong.For example, Negishi (1972) argued that since economies of scale resulting fromlearning are irreversible, if scale economies take this form one cannot suffer a loss ofscale through the resource allocation effects of trade. This misses the point. Thequestion is not where you are after trade compared with where you were before, butwhere you are after trade compared with where you would have been withouttradeand it is certainly possible to have smaller cumulative output in an industry in atrading equilibrium than you would have had if no trade had been allowed.Even if one takes care to avoid this sort of misconception, using static models tothink about dynamics can be risky. This is particularly true in imperfectly competitivemarkets, where games over time can have many possibilities not seen in one-periodgames. We do not think that this makes static analysis valueless, but a major goal offurther work will have to be to develop a truly dynamic trade theory.

2.5 Specific Inputs and Integrated FirmsOne of the most striking omissions from the theory presented in chapter 1 was anydescription of the size or character of firms. In a constant returns world of coursenothing can be said about these questions because firms are irrelevant to theequilibrium. In real-world discussions of trade, however, firms are highly visiblefeatures of the landscape. The size and character of firms are widely believed tomatter, especially when the boundaries of firms extend across national boundaries sothat firms become multinational.The theory of the firm is not as well developed as we might like it to be. One stronginsight does stand out from the work of such authors as Williamson (1975). This isthe role of specific inputs in giving rise to integrated firms.


Suppose that technology dictates that only a small number of firms produce an inputthat is highly specific to an activity which itself is carried out by only a few firms.Then there will be a strong incentive to create integrated firms producing their ownspecific inputs. Otherwise, firms will be confronted with what Williamson has calledthe ''horrors of bilateral monopoly'' where determination of the price and output ofthe specific inputs becomes the subject of a bargaining game. This game is likely tobe costly either through failure to reach agreement or through failure to reach anefficient agreement.The important implication for our purposes is the following. Suppose there is an"upstream" activity such as operation of a headquarters, which is highly specific tosome "downstream" activity, such as production of a differentiated product. Supposealso that both activities are subject to economies of scale. Then there is apresumption that both activities will be carried out by an integrated firm. In chapters12 and 13 we will use this insight as the basis for an analysis of the role ofmultinational firms.

2.6 ConclusionsThe main purpose of this chapter has been to stress that assumptions abouttechnology and market structure are not independent and to motivate the particularapproaches we take in the rest of the book. Ideally we would like to be able toprovide a complete mapping from technology to market structure. We cannot do this,presumably because not enough is yet known about such issues as the roles oftransaction costs and the costs of coordination and control. But we can limit therange of possibilities in a significant and useful way. Internal scale economies mustinvolve imperfectly competitive markets; monopoly profits may be earned by firmsunless they are eliminated by entry. And the existence of specific inputs producedwith increasing returns creates a presumption for the existence of integrated firms.

ReferencesBaumol, William J., Panzar, John C., and Willig, Robert D. Contestable Markets andthe Theory of Industry Structure. New York: Harcourt Brace Jovanovich, 1982.Either, Wilfred J. "Internationally Decreasing Costs and World Trade." Journal ofInternational Economics 9 (1979): 1-24.Hanoch, Giora. "The Elasticity of Scale and the Shape of Average Costs." AmericanEconomic Review 65 (1975): 492-497.Marshall, Alfred. Principles of Economics. London: Macmillan, 1920.


Negishi, Takashi. General Equilibrium Theory and International Trade. Amsterdam:North Holland, 1972.Ohlin, Bertil. International and Interregional Trade. Cambridge, Mass.: HarvardUniversity Press, 1933.Scherer, Fredrich. Industrial Market Structure and Economic Performance. Chicago:Rand McNally, 1980.Williamson, Oliver. Markets and Hierarchies. New York: Norton, 1975.



IIHOMOGENEOUS PRODUCTSIn this part we present three alternative approaches to modeling trade in a worldwith increasing returns. Chapter 3 presents the traditional approach, that ofassuming that increasing returns arise solely from external economies, so thatperfect competition can be preserved. Chapter 4 presents an alternative whichsometimesbut not alwaysyields similar results, that of assuming that the threat ofentry in effect constrains imperfect competitors to price at average cost. These twochapters make assumptions that minimize the importance of imperfect competitionand focus on increasing returns. Chapter 5 reverses priorities and considers ratherthe implications of oligopolistic competition.There are important differences between these different approaches. The mainmessage of this part is that there are also important similarities in both thepredictions of these approaches and the methods of analyses we use.



3External EffectsThe traditional way to model trade in the presence of increasing returns has been toassume that these scale economies are external to the firm. This assumption hasbeen historically favored because it allows one to avoid the problem of marketstructure: with external economies one can preserve the assumption of perfectcompetition.Much of the point of this book is that there are other modeling devices; perfectcompetition is not the only market structure in which to address the analysis of tradeunder increasing returns. Nevertheless, it is useful to begin with a reconsideration ofthe external effects approach. For one thing it is possible both to streamline and togeneralize this approach; since external effects are a real issue, such an improvedstatement of the model is useful. At the same time the external effects model will beuseful as a benchmark for evaluation of other approaches.In this chapter then we develop a model of production that allows for quite generalexternal affects. Special cases of these effects, which have been used extensively inthe literature, are explained and discussed. We formulate conditions for gains fromtrade for economies with this production structure and relate them to existingresults. Then we describe a variety of circumstances where we can predict tradepatterns on the basis of cross-country differences in the composition of factorendowments and describe the difficulties that arise in other cases. Examples areused to illustrate some of these points.

3.1 Production FunctionsThe production function of a representative firm in sector i of country j, is assumed todepend on a worldwide vector of extenal effects x and on the vector of inputs viemployed by the firm. Letting x1 be the firm's output level, we have



where is strictly quasiconcave and positively linear homogeneous in vi, with non-negative marginal products of vi.The vector of external effects x describes all the elements in the world economy thatcan potentially affect productivity of a firm in any sector and any country. Thus, if theworldwide size of the electronics industry affects productivity of electronicsproduction in Japan, then this size variable is an element of x. And if the size of theIsraeli sector that produces oranges affects productivity of oranges in Israel, then thesize of this sector is also an element of x. Similarly, if the employment level of aparticular factor of production in the chemical industry affects productivity ofchemical product firms, then this employment level is an element of x, and

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Market Structure and Foreign Trade- Elhanan Helpman, Paul Krugman